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My favourite IIT-JEE Maths question

Although I'm in Class 12,but I couldn't stop myself from taking a glance at this year's JEE Math's questions. I found this question to be very intriguing and so I thought of sharing it with my Brilliant friends.

For \(a \in R\) (set of real numbers) , \(a \neq -1\), \[lim_{n \to \infty}\frac{1^a+2^a+ \ldots +n^a}{(n+1)^{a-1}[(na+1)+(na+2)+\ldots+(na+n)]}= \frac{1}{60}\] Then \(a=?\)

Note by Shubham Srivastava
4 years, 3 months ago

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The answers are 7 and \(\frac{-17}{2}\). The trick here was to first express the limit in form of summation(\(\Sigma\)) and then change summation in definite integration(\(\int_0^1\)).

Shubham Srivastava - 4 years, 3 months ago

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Write a comment or ask a question...can you give me the solution

Ayobami Salau - 2 years ago

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i just did trail and error....

Gunadeep Reddy - 4 years, 3 months ago

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a=7 is only accepted

Aditya Vaikunt - 1 year, 6 months ago

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I got two answers....a=7 and a= -7/5, but the answer key gives only one. I got a quadratic equation at the end.

Anybody else got the same result?

Rish Malviya - 4 years, 3 months ago

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what's JEE?

Catherine Wooller - 4 years, 3 months ago

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It's the most competitive Engineering Entrance Exam in India.It questions on Physics,Chemistry and Mathematics......

Aahitagni Mukherjee - 4 years, 3 months ago

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joint entrance examinations

Swastik Mahapatra - 3 years, 10 months ago

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You got it?

Aabhas Mathur - 4 years, 3 months ago

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how?

Kiran Patel - 4 years, 3 months ago

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a=7

Gunadeep Reddy - 4 years, 3 months ago

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were there any options given??

Gunadeep Reddy - 4 years, 3 months ago

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Yes, its a multiple correct answers question.

Shubham Srivastava - 4 years, 3 months ago

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how to improve maths skill

Chandana Pechetti - 2 years, 9 months ago

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they really gave such easy questions this year?JEE has been diluted.

Aahitagni Mukherjee - 4 years, 3 months ago

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Good thing you didn't see the Physics section...

Rish Malviya - 4 years, 3 months ago

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I took a look,and I see no reason of deviating from my stand.I didn't see anything much innovative,except for a hydrostatics problem in paper 1,and a couple of matching type questions in paper 2.Even those were not really tough,just needed keeping your head cool.Trust me,JEE has seen much better days.

Aahitagni Mukherjee - 4 years, 3 months ago

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the chemistry questions were tough, but the maths and the physics questions were found very easy to me.

Shourya Pandey - 4 years, 3 months ago

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